A rocket of proper length 40 m is observed to be 32 m long as it rushes past the earth. What is its speed relative to the earth?

A laser beam moving at velocity c relative to us is turned on just as three (hypothetical) observers pass by us in the same direction as the beam. Observer 1 has velocity c/2, observer 2 has velocity 0.999c, and observer 3 has velocity c. If metersticks had different lengths in different frames, or clocks ticked at different rates in different frames, it is not impossible that the first and second observers could measure the beam to be moving at speed c relative to them, but the third observer could not find that the beam is moving at speed c relative to her. Prove this quantitavely.

In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.56c. He measures a trip as having a distance of 4.19e+05 m. How much time does Quicksilver measure this trip as taking? Does Quicksilver measure the proper or dilated time? Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? What distance does Wanda measúre for Quicksilver's trip?

There is a spaceship that moves past us with a speed of (3/5)c and it has a rest length of 1000 m. Two clocks on the ship's nose and tail have been synchronized with each other in the ship's frame of reference. (On the ground, we have many clocks that are synchronized with each other in our frame.) When the nose of the spaceship reaches us, both our clock as well as the clock in the ship's nose read t = 0. At this time (t = 0 to us), what will the clock in the ship's tail read and in what time will the tail reach us?